In image acquisition systems, desired system performance can be achieved by optimizing one or more design parameters. One particular parameter that it may be desirable to optimize in some image acquisition systems is depth of focus. The depth of focus of an image acquisition system is the range of distances in object space in which objects are considered to be in focus. In some image acquisition systems, such as those used for surveillance and biometric identification, it is important that the image acquisition system be capable of producing clear images of objects located at different distances from the image plane. However, conventional image acquisition systems have limited depth of focus. As a result, only objects at a fixed predetermined distance from the lens will appear in focus.
One method improving the depth of focus is to reduce the size of the lens aperture. However, reducing the lens aperture size reduces flux collected by the imaging system and increases distortion in the final image caused by diffraction.
Another method for improving depth of focus of the image acquisition system is to provide a lens that moves relative to the image plane and thereby mechanically increases the depth of focus. However, mechanically focusing an image acquisition system using moving parts may be undesirable in surveillance systems because the motion or the sound made by the moving parts may be detected by the party under surveillance. In addition, the mechanical parts used to move the lens and/or the image plane are subject to wear and may increase the overall cost of the image acquisition system. Another problem with image acquisition systems that use moving parts to focus on objects at different distances is that they are incapable of simultaneously capturing in-focus images of objects at different distances from the lens.
In light of the difficulties associated with conventional image acquisition systems, wavefront encoding methods have been developed to reduce the spatially varying blur in an acquired image caused by objects being located at different depths. Current wavefront encoding methods involve placing a cubic phase mask in front of the lens to alter the phase of incident light based a weighting factor and the cube of the x and y coordinates of each point. The mathematical expression for the phase variation produced by one common cubic mask is as follows:Φ(x,y)=a(x3+y3),  (1)where Φ(x,y) is the amount of phase variation applied by the cubic mask to each point (x,y) in the point in the image plane, x and y are the Cartesian coordinates of each point in the image plane, with (0,0) being the center of the image plane, and a is the weighting factor or strength of the mask.
FIG. 1A illustrates image blurring caused by an optical system with limited depth of focus. In FIG. 1A, the objects being imaged are two children's toys, Sylvester® the Cat and a dog, located at different focal distances. Because the optical system has limited depth of focus, the image of Sylvester® appears in focus, and the image of the dog appears out of focus. FIG. 1B is an intermediate image illustrating the results of applying a cubic mask to the same scene. In FIG. 1B, the images of the dog and Sylvester® are blurred equally. Spatially invariant blurring allows restoration by applying a common restoration algorithm to all pixels in the intermediate image. FIG. 1C illustrates the results of applying the restoration algorithm to the blurred image of FIG. 1B. In FIG. 1C, the images of the dog and Sylvester® are both in focus. Thus, from FIGS. 1A-1C, a cubic mask is capable of improving the depth of focus of an image acquisition system.
While cubic masks reduce the spatial variance in defocus caused by objects being located at different distances, simulations have shown that cubic masks can produce artifacts in the restored images, such as stripe patterns or bright streaks, which bear no resemblance to the true object being imaged. Another problem associated with cubic masks is that iterative optimization methods described herein have used cubic masks as a basis function and did not converge to the cubic mask as the optimal result. If the cubic mask were the optimal solution, the iterative optimization process would converge to the cubic mask as its solution. Thus, depending on the optimization method being used, cubic masks are not the optimal choice for phase encoding of an incident image so that an image of the original object can be produced from the phase-encoded image.
Yet another problem with phase encoding in general is that there has been no well-defined methodology for optimizing phase variation in the image plane using basis functions with multiple free parameters. For example, if a cubic phase mask is utilized, the only parameter to be selected is the weighting parameter a. Using a cubic phase mask with a single free parameter oversimplifies the filter design problem and can result in suboptimal phase masks.
Accordingly, in light of these difficulties associated with conventional phase masks and methods for designing such masks, there exists a long felt need for improved methods and systems for designing electromagnetic wave filters and for filters designed using the methods and systems.